Fleet Heterogeneity

Here I show a simple example where there are two kinds of boats harvesting over the same map. One boat has large (500 units of fish) hold while the other has only 10 units. Everything else is the same. Using fixed biomass where more fish lives farther from the coast we get that the two fleets split:

The large boats go fish farther from port while the small one fish close (since going far away means catching more than what can be brought back). A relatively obvious result.

Now imagine that we implement an arbitrary ITQ where each fisher is given quotas for 5000 units of catch. Boats with larger holds tend to be more efficient (as they spend less time travelling back and forth) and this advantage increases the more oil prices increase.
Because of the way ITQs work this translates into more quotas being bought and consumed by big boats.

Optimal MPA

Now imagine a slightly more complicated problem. The fish grows logistically and is affected by fishing. There is still more fish the farther away from the coast you tow. There are two fleet, each of 50 fishers. One is made of boats with efficient gear (catchability \(.01\), hold size \(500\) units, almost infinite fuel) while another fleet is made of boats with very inefficient gear (catchability \(.001\), hold size \(10\) and fuel enough for only very short trips).

Imagine that we want an efficient fishery (in terms of cumulative catches over 20 years) but we would also like to protect the livelihood of the smaller boats.
In particular assume we can build 1 MPA where small boats can fish but large boats cannot; how to balance efficiency and small boats income?
This is a multi-objective optimization and after 10 generations we get the following pareto-front:

There is clearly a very strong tradeoff between efficiency and small fishermen protection.

To give you an idea of what these solutions mean, this video shows how the rightmost solution looks like (the solution that maximizes small fishermen income but has very low efficiency):

That is a large MPA is built around the port. This way the fleet split between small ones that fish very near port and efficient ones who are left with only a small portion of the sea and resort to fish the line.
Notice that there is a large buffer between the two groups which provide the biomass with a sanctuary where to grow, replenishing areas around the port as they deplete.

If we look instead at the leftmost solution (most efficient, lowest in small fishers’ income) we see that the MPA is very far out to sea. This makes sense from an efficiency perspective as those areas have higher carrying capacity and can provide a lot of fish if protected. It provides no protection for small boats however who have to compete with large boats around the port initially and once those areas are depleted the smaller boats make no more significant landings.